# title
Large deviations of square root insensitive random sums

# abstract
<jats:p> We provide a large deviation result for a random sum [Formula: see text], where N<jats:sub>x</jats:sub> is a renewal counting process and {X<jats:sub>n</jats:sub>}<jats:sub>n0</jats:sub> are i.i.d. random variables, independent of N<jats:sub>x</jats:sub>, with a common distribution that belongs to a class of square root insensitive distributions. Asymptotically, the tails of these distributions are heavier than e<jats:sup>x</jats:sup> and have zero relative decrease in intervals of length x, hence square root insensitive. Using this result we derive the asymptotic characterization of the busy period distribution in the stable GI/G/1 queue with square root insensitive service times; this characterization further implies that the tail behavior of the busy period exhibits a functional change for distributions that are lighter than e<jats:sup>x</jats:sup>. </jats:p>

# publisher.label
Institute for Operations Research and the Management Sciences (INFORMS)